Find the vector and Cartesian equations of the line passing through the points A(3, 4, -6) and B(5, -2, 7).

Given: line passes through the points (3, 4, -6) and (5, -2, 7)


To find: equation of line in vector and Cartesian forms


Formula Used: Equation of a line is


Vector form:


Cartesian form:


where is a point on the line and with b1 : b2 : b3 being the direction ratios of the line.


Explanation:


Here,


The direction ratios of the line are (3 - 5) : (4 + 2) : (-6 - 7)


⇒ -2 : 6 : -13


⇒ 2 : -6 : 13


So,


Therefore,


Vector form:



Cartesian form:



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